44
SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09 Overview: This Mathcad worksheet is intended to analyze gusset plates using Load Factor Design. Gusset plates are analyzed for shear and axial force effects by the conventional "Method-of-Section" procedures. It should be noted that this Mathcad worksheet only investigates three common sections of interest, two vertical and one horizontal section. Additional sections should be investigated at joints that have a break in the alignment of the chord and/or unusual joint configurations. Member connections are analyzed for bolt/rivet capacity, block shear capacity and Whitmore section stresses. The calculations assume each truss member is connected to each gusset plate if more than one gusset plate is entered (N). The bottom chord is assumed continuous (either spliced or non-jointed) across the panel point. The calculations do not check the base material capacity of the truss members. Disclaimer: This worksheet and sample calculations outline an acceptable method for analyzing the capacity of existing truss gusset plates. There may be other acceptable procedures for this analysis. While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset plate analysis. Sound engineering judgement is required to apply this method to individual situations and to bridges that may vary from this example. Revisions: The February 2009 Baker Revision included the following additional calculations and modifications to the MathCAD file provided by VDOT: - Added Exterior/End Fastener Capacity - Added Truss Member base material check - Modified the file such that Tension and Compression checks are completed for each member - Added Rating Factor Summaries for each member - Added Controlling Member Designation in the Rating Summary - Added input for Member Force Reduction due to Chord Splice Plates - Added controlling failure check (Block Shear vs. Net Section Fracture) 01005_Gusset_U1_LFD_final Page 1 of 50

Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

  • Upload
    lyliem

  • View
    230

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Overview: This Mathcad worksheet is intended to analyze gusset plates using LoadFactor Design. Gusset plates are analyzed for shear and axial force effects by theconventional "Method-of-Section" procedures. It should be noted that this Mathcadworksheet only investigates three common sections of interest, two vertical and onehorizontal section. Additional sections should be investigated at joints that have a breakin the alignment of the chord and/or unusual joint configurations. Member connectionsare analyzed for bolt/rivet capacity, block shear capacity and Whitmore section stresses.

The calculations assume each truss member is connected to each gusset plate if morethan one gusset plate is entered (N). The bottom chord is assumed continuous (eitherspliced or non-jointed) across the panel point. The calculations do not check the basematerial capacity of the truss members.

Disclaimer: This worksheet and sample calculations outline an acceptable method foranalyzing the capacity of existing truss gusset plates. There may be other acceptableprocedures for this analysis. While this Mathcad sheet has been checked, it should beused by an engineer familiar with truss and gusset plate analysis. Sound engineeringjudgement is required to apply this method to individual situations and to bridges thatmay vary from this example.

Revisions: The February 2009 Baker Revision included the following additionalcalculations and modifications to the MathCAD file provided by VDOT:

- Added Exterior/End Fastener Capacity- Added Truss Member base material check- Modified the file such that Tension and Compression checks are completed for eachmember- Added Rating Factor Summaries for each member- Added Controlling Member Designation in the Rating Summary- Added input for Member Force Reduction due to Chord Splice Plates- Added controlling failure check (Block Shear vs. Net Section Fracture)

01005_Gusset_U1_LFD_final Page 1 of 50

Page 2: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

EXAMPLE:

kip 1000 lbf Ton 2000 lbf

Span 75 ft HS 36 Ton Input the tonnage for the vehicle,ex.(HS 20 Truck = 36 ton)

Enter 0 if live loads already include impact. Otherwise Enter 1 MI 1

Impact Factor IM50

Span1

ft 125

MI IM 0.25 (ALFD 3.8.2.1)

Figure-1 (For reference only)

Distribution Factor for the truss where the Gusset Plate is located: DF 1.06

Multiple Presence Factor m 1.0 (ALFD 3.12.1)

01005_Gusset_U1_LFD_final Page 2 of 50

Page 3: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

01005_Gusset_U1_LFD_final Page 3 of 50

Page 4: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

01005_Gusset_U1_LFD_final Page 4 of 50

Page 5: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Member Loads: Sign convention: (+) Compression, (-) Tension

Chord splices (when applicable): To determine the forces transferred to the gusset plate(s) from members 4 and5, reduce the total chord force by the capacity of the splice plates. For example, if the capacity of the spliceplates is 43% of the total chord force, then 57% of the total chord force is carried by the gusset plate.

Member (1) Member (2) Member (3) Member (4) Member (5)

Dead Loads:

Live Loads:

Chord SpliceData:

MemberThickness:

P1DL 51.28 kip P2DL 26.73 kip P3DL 101.53 kip P4DL 125.17 kip P5DL 0 kip

P1LL 59.71 kip P2LL 35.6 kip P3LL 84.82 kip P4LL 99.96 kip P5LL 0 kip

Percentage of Force carried bythe Gusset Plate: GP4 100 % GP5 0 %

Percentage of Force transferedby the Fasteners:

BP4 100 % BP5 0 %

mt15

16in mt2

3

8in mt3

0.24

1in mt4

0.24

1in mt5

0

0in

Note: The input format for live load forces are intended to be for a single truck or lane without impact. If liveload forces already include distribution factors, set DF and m in previous page to 1. Live loads should notcorrespond to a specific live load case (i.e., maximum values for each member should be entered).

Vertical and Diagonal Member Components:

X1 15 ft Y1 10.5 ft LP1 X12

Y12

LP1 18.31 ft

X2 0 ft Y2 10.5 ft LP2 X22

Y22

LP2 10.5 ft

X3 15 ft Y3 10.5 ftLP3 X3

2Y3

2

LP3 18.31 ft

Gusset Plate Properties:

Number of gusset plates: N 2 Thickness of gusset plate: gt1

2in

Depth of gusset plate: gd 2.167 ft Width of gusset plate: gw 4.167 ft

Depth of the chord member: Cdepth 10 in Width of vertical member: wvertical 6.25 in

Unsupported length for Section A-A,B-B & C-C (Distance between bolts asshown in Figure 2):

gulAA 15.5 in gulBB 9.5625 in gulCC 23.0625 in

Effective length factor: k 1.2 (ALFD 10.54.12)

Corrosion of Gusset along thesection (Average thickness):

CAA 0.0 in CBB 0.0 in CCC 0.0 in

01005_Gusset_U1_LFD_final Page 5 of 50

Page 6: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Fastener details: Corrosion in the bolts should be accounted in the diameter of the bolt

Diameter of fasteners: ϕb 0.75 in Aboltπ

4ϕb

2 Abolt 0.442 in

2

Alternate diameter of fastenersif more than one diameter is used: ϕb2 0 in Abolt2

π

4ϕb2

2 Abolt2 0 in

2

In calculating the effective gross section yeild resistance, if the area of the net section isless than 85% of the gross area, gross area is reduced by that % difference. β 0.15

Member (1) Member (2) Member (3) Member (4) Member (5)

Area of fasteners: Af1 Abolt Af2 Abolt Af3 Abolt Af4 Abolt Af5 Abolt

Member connection details:

Fastener shear:

Number of fasteners: Nf1 12 Nf2 9 Nf3 19 Nf4 18 Nf5 0

Number of endfasteners : Nendf1 2 Nendf2 2 Nendf3 3 Nendf4 3 Nendf5 0

Number of shearplanes per fastener:

Nshear1 1 Nshear2 1 Nshear3 1 Nshear4 1 Nshear5 0

Bearing of fasteners:

Avg. clear distancebetween holes(spa. - (b + 1/16"):

Lc1 1.675 in Lc2 1.563 in Lc3 1.780 in Lc4 1.767 in Lc5 0 in

Avg. end distancefrom holes to edgeof plate

Lce1 0.969 in Lce2 1.16 in Lce3 0.594 in Lce4 1.594 in Lce5 0 in

(Edge Distance - 1/2(b + 1/16"):

Avg. end distancefrom holes to edgeof truss member

Lcem1 0.969 in Lcem2 1.16 in Lcem3 0.594 in Lcem4 1.594 in Lcem5 0 in

(Edge Distance - 1/2(b + 1/16"):

Block Shear:

Length in tension, Lt:(Gusset Plate)

Lt1 5.3125 in Lt2 4.62 in Lt3 6.74 in Lt4 6.70 in Lt5 0 in

Length in tension, Ltm:(Truss Member)

Ltm1 2.890 in Ltm2 2.663 in Ltm3 6.74 in Ltm4 6.70 in Ltm5 0 in

01005_Gusset_U1_LFD_final Page 6 of 50

Page 7: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear (continued):

Number of holesalong Lt:

NholesT1 2 NholesT2 2 NholesT3 3 NholesT4 3 NholesT5 0

Length in shear, Lv1:(Gusset Plate)

Lv11 13.75 in Lv12 11.5 in Lv13 11.95 in Lv14 14.875 in Lv15 0 in

Length in shear, Lvm1:(Truss Member)

Lvm11 13.75 in Lvm12 11.5 in Lvm13 11.95 in Lvm14 14.875 in Lvm15 0 in

Number of holesalong Lv1:

NholesV11 6 NholesV12 5 NholesV13 5 NholesV14 6 NholesV15 0

Length in shear, Lv2: Lv21 13.75 in Lv22 8.4375 in Lv23 19.0625 in

Length in shear, Lvm2: Lvm21 13.75 in Lvm22 8.4375 in Lvm23 19.0625 in Lvm24 0 in Lvm25 0 in

Number of holesalong Lv2:

NholesV21 6 NholesV22 4 NholesV23 8 NholesV24 0 NholesV25 0

Gross Section Yielding:

Whitmore sectionlength: Lws1 17.875 in Lws2 13.75 in Lws3 15 in Lws4 16.625 in Lws5 0 in

Unbraced length: Lub1 11.5625 in Lub2 3.0 in Lub3 4.81 in Lub4 3.13 in Lub5 0 in

Member Fractrure:

Anet1 6.17 in2

Anet2 6.93 in2

Anet3 7.15 in2

Anet4 6.96 in2

Anet5 0 in2

Average thickness of corrosion (inches) to the gusset plate at the bolt locations in each member.

C1 0.0 in C2 0.0 in C3 0.0 in C4 0.0 in C5 0.0 in

Average thickness of corrosion (inches) to the truss member at the bolt locations in each member.

Cm1 0.0 in Cm2 0.0 in Cm3 0.12 in Cm4 0 in Cm5 0 in

01005_Gusset_U1_LFD_final Page 7 of 50

Page 8: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

ALLOWABLE STRESSES:

Truss Member Properties:

Fy - Member: Fym1 30000 psi Fym2 30000 psi Fym3 30000 psi Fym4 30000 psi Fym5 30000 psi

Fu - Member: Fum1 60000 psi Fum2 60000 psi Fum3 60000 psi Fum4 60000 psi Fum5 60000 psi

Gusset Plate Properties:

Fy 30000 psi For members with unknown properties, see Table 6.6.2.1-2 in AASHTO Manual forCondition Evaluation of Bridges.

FU 60000psi Specified minimum tensile strength of the connected material

Following are the four levels of rating in LFD method. Dead load and live load factors vary for these ratings:

1 -Inventory2 -Operating

Case Dead Load Factors Live Load Factors

σ1

Fy DL1

1.3 LL1

2.17

σ2

Fy DL2

1.3 LL2

1.3

In Axial Tension: ften Fy

In Shear: fv

Fy

1.35 3

Modulus of elasticity: Es 29000000 psi

Design Strength of Fasteners: σDesign 18000 psi Shown for Power Driven Rivets ASTM A502,Shear - Grade 2, (ALFD Table 10.56A)

01005_Gusset_U1_LFD_final Page 8 of 50

Page 9: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Connection Analysis:

FORCE CONVENTION: TENSION (-) COMPRESSION (+).

P1DL P1DL P1LL m DF 1 IM( ) P1LL

P1DL 51.28 kip P1LL 79.12 kip

M1T "MEMBER IS IN TENSION, TENSION CHECK IS REQUIRED"

Analysis of Gusset Plate @ Diagonal (Member 1): (TENSION CHECK)

Figure-3

Fastener Capacity: (Tension or Compression)

Shear in fasteners:

Shear Area: Ashear Nf1 Abolt Ashear 5.3 in2

Shear Capacity: Cshear σDesign Ashear N Nshear1 Cshear 191 kip

01005_Gusset_U1_LFD_final Page 9 of 50

Page 10: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕR min 0.9 Lc1 gt C1 FU 1.8 ϕb gt C1 FU ϕR 40.5 kip (ALFD 10-166b)

Fastener Capacity: Cbearing Nf1 Nendf1 ϕR Cbearing 405 kip

Bearing of fasteners (END) (AASHTO 10.56.1.3):

ϕRend min 0.9 Lce1 gt C1 FU 1.8 ϕb gt C1 FU ϕRend 26.16 kip (ALFD 10-166b)

Fastener Capacity: Cendbearing Nendf1 ϕRend Cendbearing 52 kip

Bearing of fasteners - Controlling Ccontrolling min Cshear 2 Cbearing Cendbearing

Ccontrolling 190.85 kipRatings (Tons)

RFastener1j

0.9Ccontrolling DLj

P1DL

LLj

P1LLHS

RFastener1

1

12

22.036.8

Ton

Rating Factors

RFFastener1j

0.9Ccontrolling DLj

P1DL

LLj

P1LL

RFFastener1

1

12

0.61.0

Block Shear Capacity:

AShear Lv11 NholesV111

2

ϕb1

8in

Lv21 NholesV211

2

ϕb1

8in

gt C1 N

AShear 17.88 in2

ATension Lt1 NholesT1 1 ϕb1

8in

gt C1 N ATension 4.44 in2

Block Shear Capacity:

C 0.85 0.58 Fy Lv11 Lv21 gt C1 N FU ATension ATension 0.58 AShearif

0.85 0.58 FU AShear Fy Lt1 gt C1 N otherwise

C 664 kip

01005_Gusset_U1_LFD_final Page 10 of 50

Page 11: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Ratings (Tons)

RTen.block1jif P1DL 0 "NA"

0.9C DLj

P1DL

LLj

P1LLHS( )

RTen.block1

1

12

111.4185.9

Ton

Rating Factors

RFTen.block1jif P1DL 0 "NA"

0.9C DLj

P1DL

LLj

P1LL

RFTen.block1

1

12

3.15.2

Tension Capacity of the Gusset plate (Whitmore Section):

Ae min Lws1 gt C1 Lws1 NholesT1 ϕb1

8in

gt C1 β Lws1 gt C1

Ae 8.94 in2

Stress due to Dead Load: σDL

P1DL

N Ae σDL 2869 psi

Stress due to Live Load: σLL

P1LL

N Ae σLL 4426 psi

Ratings (Tons)

RYielding1jif P1DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLLHS( )

RYielding1

1

12

87.2145.6

Ton

Rating Factors

RFYielding1jif P1DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLL

RFYielding1

1

12

2.44.0

01005_Gusset_U1_LFD_final Page 11 of 50

Page 12: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M1C "MEMBER IS IN TENSION, COMPRESSION CHECK IS NOT REQUIRED"

Analysis of Gusset Plate @ Diagonal (Member 1): (COMPRESSION CHECK)

Note: See Tension Check for Fastener Capacity

Compression Capacity of the Gusset plate (Whitmore Section):

Stress due to Dead Load: σDL

P1DL

N Lws1 gt C1 σDL 2869 psi

Stress due to Live Load: σLL

P1LL

N Lws1 gt C1 σLL 4426 psi

Allowable compressive stresses (ALFD 10.54.1.1): FHWA Guidelines calculate the unbraced length asthe average of three distances. Using the unbraced length along the line of action, as done here, shouldprovide conservative ratings.

L Lub1 k 1.20 rgt C1 2

12

r 0.14 in

.

cc

2 π( )2

Es

Fy cc 138.1

k L

r96.1

FaLd 0.85Fy 1

k L

r

2

Fy

4 π( )2

Es

k L

rccif

0.85π( )

2Es

k L

r

2

otherwise

FaLd 19325 psi

Ratings (Tons)

RBuckling1jif P1DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLLHS( )

RBuckling1

1

12

"NA""NA"

Ton

Rating Factors

RFBuckling1jif P1DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLL

RFBuckling1

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 12 of 50

Page 13: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M1T "MEMBER IS IN TENSION, TENSION CHECK IS REQUIRED"

Analysis of Diagonal Truss Member (Member 1):

Fastener Capacity:

Note: Shear in Fasteners is the same as in the Gusset Plate (See Gusset Plate Calcs)

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕRmember min 0.9 Lc1 mt1 Cm1 Fum1 1.8 ϕb mt1 Cm1 Fum1 (ALFD 10-166b)

ϕRmember 25.31 kip

Fastener Capacity:Cmbearing Nf1 Nendf1 ϕRmember Cmbearing 253 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRmemberend min 0.9 Lcem1 mt1 Cm1 Fum1 1.8 ϕb mt1 Cm1 Fum1 (ALFD 10-166b)

ϕRmemberend 16.35 kip

Fastener Capacity:Cmendbearing Nendf1 ϕRmemberend Cmendbearing 33 kip

Fasteners - Controlling Cmcontrolling min Cshear 2 Cmbearing Cmendbearing

Cmcontrolling 190.85 kip

Ratings (Tons)

RmFastener1j

0.9Cmcontrolling DLj

P1DL

LLj

P1LLHS

RmFastener1

1

12

22.036.8

Ton

Rating Factors

RFmFastener1j

0.9Cmcontrolling DLj

P1DL

LLj

P1LL RFmFastener1

1

12

0.61.0

01005_Gusset_U1_LFD_final Page 13 of 50

Page 14: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AmShear Lvm11 NholesV111

2

ϕb1

8in

Lvm21 NholesV211

2

ϕb1

8in

mt1 Cm1 N

AmShear 11.17 in2

AmTension Ltm1 NholesT1 1 ϕb1

8in

mt1 Cm1 N AmTension 1.26 in2

Block Shear Capacity:

CBlockShear 0.85 0.58 Fym1 Lvm11 Lvm21 mt1 Cm1 N Fum1 AmTension AmTension 0.58 AmShearif

0.85 0.58 Fum1 AmShear Fym1 Ltm1 mt1 Cm1 N otherwise

CBlockShear 377 kip

CFracture Fum1 Anet1 CFracture 370.2 kip

Cm min CBlockShear CFracture Cm 370.2 kip

Ratings (Tons)

RmTen.block1jif P1DL 0 "NA"

0.9Cm DLj

P1DL

LLj

P1LLHS( )

RmTen.block1

1

12

55.993.3

Ton

Rating Factors

RFmTen.block1jif P1DL 0 "NA"

0.9Cm DLj

P1DL

LLj

P1LL

RFmTen.block1

1

12

1.62.6

01005_Gusset_U1_LFD_final Page 14 of 50

Page 15: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

P2DL P2DL P2LL m DF 1 IM( ) P2LL

P2DL 26.73 kip P2LL 47.17 kip

M2T "MEMBER IS IN TENSION, TENSION CHECK IS REQUIRED"

Analysis of Gusset Plate @ Vertical (Member 2): (TENSION CHECK)

Fastener Capacity:

Shear in fasteners:

Shear Area: Ashear Nf2 Abolt Ashear 3.98 in2

Shear Capacity: Cshear σDesign Ashear N Nshear2 Cshear 143 kip

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕR min 0.9 Lc2 gt C2 FU 1.8 ϕb gt C2 FU ϕR 40.5 kip (ALFD 10-166b)

Fastener Capacity: Cbearing Nf2 Nendf2 ϕR Cbearing 283 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRend min 0.9 Lce2 gt C2 FU 1.8 ϕb gt C2 FU ϕRend 31.32 kip (ALFD 10-166b)

Fastener Capacity: Cendbearing Nendf2 ϕRend Cendbearing 63 kip

Bearing of fasteners - Controlling Ccontrolling min Cshear 2 Cbearing Cendbearing

Ccontrolling 143.14 kip

Ratings (Tons)

RFastener2j

0.9Ccontrolling DLj

P2DL

LLj

P2LLHS RFastener2

1

12

33.155.2

Ton

Rating Factors

RFFastener2j

0.9Ccontrolling DLj

P2DL

LLj

P2LL RFFastener2

1

12

0.91.5

01005_Gusset_U1_LFD_final Page 15 of 50

Page 16: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AShear Lv12 NholesV121

2

ϕb1

8in

Lv22 NholesV221

2

ϕb1

8in

gt C2 N

AShear 12.94 in2

ATension Lt2 NholesT2 1 ϕb1

8in

gt C2 N ATension 3.75 in2

Block Shear Capacity:

C 0.85 0.58 Fy Lv12 Lv22 gt C2 N FU ATension ATension 0.58 AShearif

0.85 0.58 FU AShear Fy Lt2 gt C2 N otherwise

C 501 kip

Ratings (Tons)

RTen.block2jif P2DL 0 "NA"

0.9C DLj

P2DL

LLj

P2LLHS( )

RTen.block2

1

12

146.2244.0

Ton

Rating Factors

RFTen.block2jif P2DL 0 "NA"

0.9C DLj

P2DL

LLj

P2LL

RFTen.block2

1

12

4.16.8

Tension Capacity of the Gusset plate (Whitmore Section):

Ae min Lws2 gt C2 Lws2 NholesT2 ϕb1

8in

gt C2 β Lws2 gt C2

Ae 6.87 in2

Stress due to Dead Load: σDL

P2DL

N Ae σDL 1944 psi

Stress due to Live Load: σLL

P2LL

N Ae σLL 3431 psi

01005_Gusset_U1_LFD_final Page 16 of 50

Page 17: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Ratings (Tons)

RYielding2jif P2DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLLHS( )

RYielding2

1

12

118.3197.6

Ton

Rating Factors

RFYielding2jif P2DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLL

RFYielding2

1

12

3.35.5

01005_Gusset_U1_LFD_final Page 17 of 50

Page 18: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M2C "MEMBER IS IN TENSION, COMPRESSION CHECK IS NOT REQUIRED"

Analysis of Gusset Plate @ Vertical (Member 2): (COMPRESSION CHECK)

Note: See Tension Check for Fastener Capacity

Compression Capacity of the Gusset plate (Whitmore Section):

Stress due to Dead Load: σDL

P2DL

N Lws2 gt C2 σDL 1944 psi

Stress due to Live Load: σLL

P2LL

N Lws2 gt C2 σLL 3431 psi

Allowable compressive stresses (ALFD 10.54.1.1): FHWA Guidelines calculate the unbraced length asthe average of three distances. Using the unbraced length along the line of action, as done here, shouldprovide conservative ratings.

L Lub2 k 1.20r

gt C2 212

r 0.14 in.

cc

2 π( )2

Es

Fy cc 138.1

k L

r24.9

FaLd 0.85Fy 1

k L

r

2

Fy

4 π( )2

Es

k L

rccif

0.85π( )

2Es

k L

r

2

otherwise

FaLd 25084 psi

Ratings (Tons)

RBuckling2jif P2DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLLHS( )

RBuckling2

1

12

"NA""NA"

Ton

Rating Factors

RFBuckling2jif P2DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLL

RFBuckling2

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 18 of 50

Page 19: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M2T "MEMBER IS IN TENSION, TENSION CHECK IS REQUIRED"

Analysis of Vertical Truss Member (Member 2):

Fastener Capacity:

Note: Shear in Fasteners is the same as in the Gusset Plate (See Gusset Plate Calcs)

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕRmember min 0.9 Lc2 mt2 Cm2 Fum2 1.8 ϕb mt2 Cm2 Fum2 (ALFDO 10-166b)

ϕRmember 30.37 kip

Fastener Capacity: Cmbearing Nf2 Nendf2 ϕRmember Cmbearing 212.625 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRmemberend min 0.9 Lcem2 mt2 Cm2 Fum2 1.8 ϕb mt2 Cm2 Fum2 (ALFD 10-166b)

ϕRmemberend 23.49 kip

Fastener Capacity: Cmendbearing Nendf2 ϕRmemberend Cmendbearing 46.98 kip

Bearing of fasteners - Controlling Cmcontrolling min Cshear 2 Cmbearing Cmendbearing

Cmcontrolling 143.14 kip

Ratings (Tons)

RmFastener2j

0.9Cmcontrolling DLj

P2DL

LLj

P2LLHS RmFastener2

1

12

33.155.2

Ton

Rating Factors

RFmFastener2j

0.9Cmcontrolling DLj

P2DL

LLj

P2LL RFmFastener2

1

12

0.91.5

01005_Gusset_U1_LFD_final Page 19 of 50

Page 20: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AmShear Lvm12 NholesV121

2

ϕb1

8in

Lvm22 NholesV221

2

ϕb1

8in

mt2 Cm2 N

AmShear 9.7 in2

AmTension Ltm2 NholesT2 1 ϕb1

8in

mt2 Cm2 N AmTension 1.34 in2

Block Shear Capacity:

CBlockShear 0.85 0.58 Fym2 Lvm12 Lvm22 mt2 Cm2 N Fum2 AmTension AmTension 0.58 AmShearif

0.85 0.58 Fum2 AmShear Fym2 Ltm2 mt2 Cm2 N otherwise

CBlockShear 338 kip

CFracture Fum2 Anet2CFracture 415.8 kip

Cm min CBlockShear CFracture Cm 337.95 kip

Ratings (Tons)

RmTen.block2jif P2DL 0 "NA"

0.9Cm DLj

P2DL

LLj

P2LLHS( )

RmTen.block2

1

12

94.8158.2

Ton

Rating Factors

RFmTen.block2jif P2DL 0 "NA"

0.9Cm DLj

P2DL

LLj

P2LL

RFmTen.block2

1

12

2.64.4

01005_Gusset_U1_LFD_final Page 20 of 50

Page 21: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

P3DL P3DL P3LL m DF 1 IM( ) P3LL

P3DL 101.53 kip P3LL 112.39 kip

M3T "MEMBER IS IN COMPRESSION, TENSION CHECK IS NOT REQUIRED"

Analysis of Gusset Plate @ Diagonal (Member 3): (TENSION CHECK)

Fastener Capacity:

Shear in fasteners:

Shear Area: Ashear Nf3 Abolt Ashear 8.39 in2

Shear Capacity: Cshear σDesign Ashear N Nshear3 Cshear 302 kip

Bearing of fasteners (INTERIOR) (AASHTO 10.56.1.3): j 1 2

ϕR min 0.9 Lc3 gt C3 FU 1.8 ϕb gt C3 FU ϕR 40.5 kip (ALFD 10-166b)

Fastener Capacity: Cbearing Nf3 Nendf3 ϕR Cbearing 648 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRend min 0.9 Lce3 gt C3 FU 1.8 ϕb gt C3 FU ϕRend 16.04 kip (ALFD 10-166b)

Fastener Capacity: Cendbearing Nendf3 ϕRend Cendbearing 48.114 kip

Bearing of fasteners - Controlling Ccontrolling min Cshear 2 Cbearing Cendbearing

Ccontrolling 302.18 kip

Ratings (Tons)

RFastener3j

0.9Ccontrolling DLj

P3DL

LLj

P3LLHS

RFastener3

1

12

20.734.5

Ton

Rating Factors

RFFastener3j

0.9Ccontrolling DLj

P3DL

LLj

P3LL

RFFastener3

1

12

0.61.0

01005_Gusset_U1_LFD_final Page 21 of 50

Page 22: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AShear Lv13 NholesV131

2

ϕb1

8in

Lv23 NholesV231

2

ϕb1

8in

gt C3 N

AShear 20.51 in2

ATension Lt3 NholesT3 1 ϕb1

8in

gt C3 N ATension 4.99 in2

Block Shear Capacity:

C 0.85 0.58 Fy Lv13 Lv23 gt C3 N FU ATension ATension 0.58 AShearif

0.85 0.58 FU AShear Fy Lt3 gt C3 N otherwise

C 779 kip

Ratings (Tons)

RTen.block3jif P3DL 0 "NA"

0.9C DLj

P3DL

LLj

P3LLHS( )

RTen.block3

1

12

"NA""NA"

Ton

Rating Factors

RFTen.block3jif P3DL 0 "NA"

0.9C DLj

P3DL

LLj

P3LL

RFTen.block3

1

12

"NA""NA"

Tension Capacity of the Gusset plate (Whitmore Section):

Ae min Lws3 gt C3 Lws3 NholesT3 ϕb1

8in

gt C3 β Lws3 gt C3

Ae 7.31 in2

Stress due to Dead Load: σDL

P3DL

N Ae σDL 6942 psi

Stress due to Live Load: σLL

P3LL

N Ae σLL 7685 psi

01005_Gusset_U1_LFD_final Page 22 of 50

Page 23: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Ratings (Tons)

RYielding3jif P3DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLLHS( )

RYielding3

1

12

"NA""NA"

Ton

Rating Factors

RFYielding3jif P3DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLL

RFYielding3

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 23 of 50

Page 24: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M3C "MEMBER IS IN COMPRESSION, COMPRESSION CHECK IS REQUIRED"

Analysis of Gusset Plate @ Diagonal (Member 3): (COMPRESSION CHECK)

Note: See Tension Check for Fastener Capacity

Compression Capacity of the Gusset plate (Whitmore Section):

Stress due to Dead Load: σDL

P3DL

N Lws3 gt C3 σDL 6769 psi

Stress due to Live Load: σLL

P3LL

N Lws3 gt C3 σLL 7492 psi

Allowable compressive stresses (ALFD 10.54.1.1): FHWA Guidelines calculate the unbraced length asthe average of three distances. Using the unbraced length along the line of action, as done here, shouldprovide conservative ratings.

L Lub3 k 1.20r

gt C3 212

r 0.14 in.

cc

2 π( )2

Es

Fy cc 138.1

k L

r40

FaLd 0.85Fy 1

k L

r

2

Fy

4 π( )2

Es

k L

rccif

0.85π( )

2Es

k L

r

2

otherwise

FaLd 24431 psi

Ratings (Tons)

RBuckling3jif P3DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLLHS( )

RBuckling3

1

12

29.248.7

Ton

Rating Factors

RFBuckling3jif P3DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLL

RFBuckling3

1

12

0.81.4

01005_Gusset_U1_LFD_final Page 24 of 50

Page 25: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M3T "MEMBER IS IN COMPRESSION, TENSION CHECK IS NOT REQUIRED"

Analysis of Diagonal Truss Member (Member 3):

Fastener Capacity:

Note: Shear in Fasteners is the same as in the Gusset Plate (See Gusset Plate Calcs)

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕRmember min 0.9 Lc3 mt3 Cm3 Fum3 1.8 ϕb mt3 Cm3 Fum3 (ALFD 10-166b)

ϕRmember 9.72 kip

Fastener Capacity: Cmbearing Nf3 Nendf3 ϕRmember Cmbearing 155.52 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRmemberend min 0.9 Lcem3 mt3 Cm3 Fum3 1.8 ϕb mt3 Cm3 Fum3 (ALFD 10-166b)

ϕRmemberend 3.85 kip

Fastener Capacity: Cmendbearing Nendf3 ϕRmemberend Cmendbearing 11.547 kip

Bearing of fasteners - Controlling Cmcontrolling min Cshear 2 Cmbearing Cmendbearing

Cmcontrolling 302.18 kip

Ratings (Tons)

RmFastener3j

0.9Cmcontrolling DLj

P3DL

LLj

P3LLHS RmFastener3

1

12

20.734.5

Ton

Rating Factors

RFmFastener3j

0.9Cmcontrolling DLj

P3DL

LLj

P3LL RFmFastener3

1

12

0.61.0

01005_Gusset_U1_LFD_final Page 25 of 50

Page 26: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AmShear Lvm13 NholesV131

2

ϕb1

8in

Lvm23 NholesV231

2

ϕb1

8in

mt3 Cm3 N

AmShear 4.92 in2

AmTension Ltm3 NholesT3 1 ϕb1

8in

mt3 Cm3 N AmTension 1.2 in2

Block Shear Capacity:

CBlockShear 0.85 0.58 Fym3 Lvm13 Lvm23 mt3 Cm3 N Fum3 AmTension AmTension 0.58 AmShearif

0.85 0.58 Fum3 AmShear Fym3 Ltm3 mt3 Cm3 N otherwise

CBlockShear 187 kip

CFracture Fum3 Anet3 CFracture 429 kip

Cm min CBlockShear CFracture Cm 186.87 kip

Ratings (Tons)

RmTen.block3jif P3DL 0 "NA"

0.9Cm DLj

P3DL

LLj

P3LLHS( )

RmTen.block3

1

12

"NA""NA"

Ton

Rating Factors

RFmTen.block3jif P3DL 0 "NA"

0.9Cm DLj

P3DL

LLj

P3LL

RFmTen.block3

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 26 of 50

Page 27: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

P4DL P4DL P4LL m DF 1 IM( ) P4LL

P4DL 125.17 kip P4LL 132.45 kip

M4T "MEMBER IS IN COMPRESSION, TENSION CHECK IS NOT REQUIRED"

Analysis of Gusset Plate @ Left Chord (Member 4): (TENSION CHECK)

Fastener Capacity:

Shear in fasteners:

Shear Area: Ashear Nf4 Abolt Ashear 7.95 in2

Shear Capacity: Cshear σDesign Ashear N Nshear4 Cshear 286 kip

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕR min 0.9 Lc4 gt C4 FU 1.8 ϕb gt C4 FU ϕR 40.5 kip (ALFD 10-166b)

Fastener Capacity: Cbearing Nf4 Nendf4 ϕR Cbearing 607.5 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRend min 0.9 Lce4 gt C4 FU 1.8 ϕb gt C4 FU ϕRend 40.5 kip (ALFD 10-166b)

Fastener Capacity: Cendbearing Nendf4 ϕRend Cendbearing 121.5 kip

Bearing of fasteners - Controlling Ccontrolling min Cshear 2 Cbearing Cendbearing

Ccontrolling 286.28 kip

Ratings (Tons)

RFastener4j

0.9Ccontrolling DLj

P4DL BP4

LLj

P4LL BP4HS RFastener4

1

12

11.919.8

Ton

Rating Factors

RFFastener4j

0.9Ccontrolling DLj

P4DL BP4

LLj

P4LL BP4 RFFastener4

1

12

0.30.6

01005_Gusset_U1_LFD_final Page 27 of 50

Page 28: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AShear Lv14 NholesV141

2

ϕb1

8in

gt C4 N

AShear 10.06 in2

ATension Lt4 NholesT41

2

ϕb1

8in

gt C4 N ATension 4.51 in2

Block Shear Capacity:

C 0.85 0.58 Fy Lv14 gt C4 N FU ATension ATension 0.58 AShearif

0.85 0.58 FU AShear Fy Lt4 gt C4 N otherwise

C 468 kip

Ratings (Tons)

RTen.block4jif P4DL 0 "NA"

0.9C DLj

P4DL GP4

LLj

P4LL GP4 HS( )

RTen.block4

1

12

"NA""NA"

Ton

Rating Factors

RFTen.block4jif P4DL 0 "NA"

0.9C DLj

P4DL GP4

LLj

P4LL GP4

RFTen.block4

1

12

"NA""NA"

Tension Capacity of the Gusset plate (Whitmore Section):

Ae min Lws4 gt C4 Lws4 NholesT4 ϕb1

8in

gt C4 β Lws4 gt C4

Ae 8.25 in2

Stress due to Dead Load: σDL

P4DL GP4

N Ae σDL 7589 psi

Stress due to Live Load: σLL

P4LL GP4

N Ae σLL 8030 psi

01005_Gusset_U1_LFD_final Page 28 of 50

Page 29: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Ratings (Tons)

RYielding4jif P4DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLLHS( )

RYielding4

1

12

"NA""NA"

Ton

Rating Factors

RFYielding4jif P4DL 0 "NA"

0.9Fy DLj

σDL

LLj

σLL

RFYielding4

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 29 of 50

Page 30: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M4C "MEMBER IS IN COMPRESSION, COMPRESSION CHECK IS REQUIRED"

Analysis of Gusset Plate @ Left Chord (Member 4): (COMPRESSION CHECK)

Note: See Tension Check for Fastener Capacity

Compression Capacity of the Gusset plate (Whitmore Section):

Stress due to Dead Load: σDL

P4DL GP4

N Lws4 gt C4 σDL 7529 psi

Stress due to Live Load: σLL

P4LL GP4

N Lws4 gt C4 σLL 7967 psi

Allowable compressive stresses (ALFD 10.54.1.1): FHWA Guidelines calculate the unbraced length asthe average of three distances. Using the unbraced length along the line of action, as done here, shouldprovide conservative ratings.

L Lub4 k 1.20r

gt C4 212

r 0.14 in.

cc

2 π( )2

Es

Fy cc 138.1

k L

r26

FaLd 0.85Fy 1

k L

r

2

Fy

4 π( )2

Es

k L

rccif

0.85π( )

2Es

k L

r

2

otherwise

FaLd 25048 psi

Ratings (Tons)

RBuckling4jif P4DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLLHS( )

RBuckling4

1

12

26.644.3

Ton

Rating Factors

RFBuckling4jif P4DL 0 "NA"

0.9FaLd DLj

σDL

LLj

σLL

RFBuckling4

1

12

0.71.2

01005_Gusset_U1_LFD_final Page 30 of 50

Page 31: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

M4T "MEMBER IS IN COMPRESSION, TENSION CHECK IS NOT REQUIRED"

Analysis of Left Chord Truss Member (Member 4):

Fastener Capacity:

Note: Shear in Fasteners is the same as in the Gusset Plate (See Gusset Plate Calcs)

Bearing of fasteners (INTERIOR) (ALFD 10.56.1.3): j 1 2

ϕRmember min 0.9 Lc4 mt4 Cm4 Fum4 1.8 ϕb mt4 Cm4 Fum4 (ALFD 10-166b)

ϕRmember 19.44 kip

Fastener Capacity: Cmbearing Nf4 Nendf4 ϕRmember Cmbearing 291.6 kip

Bearing of fasteners (END) (ALFD 10.56.1.3):

ϕRmemberend min 0.9 Lcem4 mt4 Cm4 Fum4 1.8 ϕb mt4 Cm4 Fum4 (ALFD 10-166b)

ϕRmemberend 19.44 kip

Fastener Capacity: Cmendbearing Nendf4 ϕRmemberend Cmendbearing 58.32 kip

Bearing of fasteners - Controlling Cmcontrolling min Cshear 2 Cmbearing Cmendbearing

Cmcontrolling 286.28 kip

Ratings (Tons)

RmFastener4j

0.9Cmcontrolling DLj

P4DL BP4

LLj

P4LL BP4HS RmFastener4

1

12

11.919.8

Ton

Rating Factors

RFmFastener4j

0.9Cmcontrolling DLj

P4DL BP4

LLj

P4LL BP4 RFmFastener4

1

12

0.30.6

01005_Gusset_U1_LFD_final Page 31 of 50

Page 32: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Block Shear Capacity:

AmShear Lvm14 NholesV141

2

ϕb1

8in

Lvm24 NholesV241

2

ϕb1

8in

mt4 Cm4 N

AmShear 5.04 in2

AmTension Ltm4 NholesT4 1 ϕb1

8in

mt4 Cm4 N AmTension 2.38 in2

Block Shear Capacity:

CBlockShear 0.85 0.58 Fym4 Lvm14 mt4 Cm4 N Fum4 AmTension AmTension 0.58 AmShearif

0.85 0.58 Fum4 AmShear Fym4 Ltm4 mt4 Cm4 N otherwise

CBlockShear 231 kip

CFracture Fum4 Anet4CFracture 417.6 kip

Ratings (Tons)

RmTen.block4jif P4DL 0 "NA" min

0.9CBlockShear DLj

P4DL GP4

LLj

P4LL GP4HS( )

0.9CFracture DLj

P4DL

LLj

P4LLHS( )

RmTen.block4

1

12

"NA""NA"

Ton

Rating Factors

RFmTen.block4jif P4DL 0 "NA" min

0.9CBlockShear DLj

P4DL GP4

LLj

P4LL GP4

0.9CFracture DLj

P4DL

LLj

P4LL

RFmTen.block4

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 32 of 50

Page 33: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Section A-A: (Parallel to Chord member): Gusset Plates Subject to Horizontal Shear

AreaAA N gw gt CAA AreaAA 50 in2

Unsupported length to thickness ratio:

RatiogulAA

gt CAA Ratio 31

Edge "PASS"11000

Fy1

1 psi

Ratioif

"FAIL" otherwise

(AASHTO Guide Specificationsfor Strength Design Section 1.11)

Edge "PASS"

Summation of Horizontal Forces:

For Dead Load: PHDL P1DLX1

LP1

P2DL

X2

LP2

P3DL

X3

LP3

PHDL 41.2 kip

For Live Load: PHLL P1LLX1

LP1

P2LL

X2

LP2

P3LL

X3

LP3

PHLL 20.57 kip

01005_Gusset_U1_LFD_final Page 33 of 50

Page 34: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Gross Section Shear Yeilding Resistance:

Vrgross

AreaAA fv

N Vrgross 320.78 kip

Net Section Shear Fracture Resistance:

Vrnet

AreaAA

Ngt NholesV14 NholesV15 ϕb 0.125in

0.85 0.58 FU Vrnet 661.91 kip

Controlling Shear Resistance:

Vr min Vrgross Vrnet Vr 320.78 kip

RVrAAj

0.9Vr DLj

PHDL

N

LLj

PHLL

N

HS( ) RVrAA422.49

705.24

Ton

RFVrAAj

0.9Vr DLj

PHDL

N

LLj

PHLL

N

RFVrAA11.74

19.59

01005_Gusset_U1_LFD_final Page 34 of 50

Page 35: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

SECTION B-B: Load rating, along Section B-B

AreaBB N gd gt CBB AreaBB 26 in2

Unsupported length to thickness ratio:

RatiogulBB

gt CBB Ratio 19.13

Edge "PASS"11000

Fy1

1 psi

Ratioif

"FAIL" otherwise

(AASHTO Guide Specifications forStrength Design Section 1.11)

Edge "PASS"

Summation of Vertical Forces:

For Dead Load: PVDL P3DL

Y3

LP3

PVDL 58.2 kip

For Live Load: PVLL P3LL

Y3

LP3

PVLL 48.641 kip

01005_Gusset_U1_LFD_final Page 35 of 50

Page 36: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Gross Section Shear Yeilding Resistance:

Vrgross

AreaBB fv

N Vrgross 166.82 kip

Net Section Shear Fracture Resistance:

Use T = 1 when line through the bolts for Vertical member passesthrough the bolts for Chord member, otherwise, use T = 2.

T 2Nholes max NholesT5 NholesV22 T 1if

NholesT5 NholesV22 otherwise

Vrnet

AreaBB

Ngt Nholes ϕb 0.125in

0.85 0.58 FU Vrnet 332.83 kip

Controlling Shear Resistance:

Vr min Vrgross Vrnet Vr 166.82 kip

RVrBBj

0.9Vr DLj

PVDL

N

LLj

PVLL

N

HS( ) RVrBB76.6

127.86

Ton

RFVrBBj

0.9Vr DLj

PVDL

N

LLj

PVLL

N

RFVrBB2.13

3.55

01005_Gusset_U1_LFD_final Page 36 of 50

Page 37: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

SECTION C-C: Load rating, along Section C-C. Mirror of Section B-B

AreaCC N gd gt CCC AreaCC 26 in2

Unsupported length to thickness ratio:

RatiogulCC

gt CCC Ratio 46.13

Edge "PASS"11000

Fy1

1 psi

Ratioif

"FAIL" otherwise

(AASHTO Guide Specifications forStrength Design Section 1.11)

Edge "PASS"

Summation of Vertical Forces:

For Dead Load: PVDL P1DL

Y1

LP1

PVDL 29.4 kip

For Live Load: PVLL P1LL

Y1

LP1

PVLL 34.241 kip

Gross Section Shear Yeilding Resistance:

Vrgross

AreaCC fv

N Vrgross 166.82 kip

01005_Gusset_U1_LFD_final Page 37 of 50

Page 38: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Net Section Shear Fracture Resistance:

Use T = 1 when line through the bolts for Vertical member passesthrough the bolts for Chord member, otherwise, use T = 2.

T 2

Nholes max NholesT4 NholesV12 T 1if

NholesT4 NholesV12 otherwise

Vrnet

AreaCC

Ngt Nholes ϕb 0.125in

0.85 0.58 FU Vrnet 319.89 kip

Controlling Shear Resistance:

Vr min Vrgross Vrnet Vr 166.82 kip

RVrCCj

0.9Vr DLj

PVDL

N

LLj

PVLL

N

HS( ) RVrCC126.96

211.92

Ton

RFVrCCj

0.9Vr DLj

PVDL

N

LLj

PVLL

N

RFVrCC3.53

5.89

01005_Gusset_U1_LFD_final Page 38 of 50

Page 39: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Gusset Plate Rating Summary

Left Diagonal - Member 1 - Rating:

Block Shear Gross Section Yielding

RTen.block1

1

12

111.37185.91

Ton RYielding1

1

12

87.22145.60

Ton

RFTen.block1

1

12

3.095.16

RFYielding1

1

12

2.424.04

Buckling Fastener Capacity

RBuckling1

1

12

"NA""NA"

Ton RFastener1

1

12

22.0436.79

Ton

RFBuckling1

1

12

"NA""NA"

RFFastener1

1

12

0.611.02

Vertical - Member 2 - Rating:

Block Shear Gross Section Yielding

RTen.block2

1

12

146.20244.05

Ton RYielding2

1

12

118.35197.55

Ton

RFTen.block2

1

12

4.066.78

RFYielding2

1

12

3.295.49

Buckling Fastener Capacity

RBuckling2

1

12

"NA""NA"

Ton RFastener2

1

12

33.0955.23

Ton

RFBuckling2

1

12

"NA""NA"

RFFastener2

1

12

0.921.53

01005_Gusset_U1_LFD_final Page 39 of 50

Page 40: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Gusset Plate Rating Summary (continued)

Right Diagonal - Member 3 - Rating:

Block Shear Gross Section Yielding

RTen.block3

1

12

"NA""NA"

Ton RYielding3

1

12

"NA""NA"

Ton

RFTen.block3

1

12

"NA""NA"

RFYielding3

1

12

"NA""NA"

Buckling Fastener Capacity

RBuckling3

1

12

29.2048.75

Ton RFastener3

1

12

20.6634.49

Ton

RFBuckling3

1

12

0.811.35

RFFastener3

1

12

0.570.96

Left Chord - Member 4 - Rating:

Block Shear Gross Section Yielding

RTen.block4

1

12

"NA""NA"

Ton RYielding4

1

12

"NA""NA"

Ton

RFTen.block4

1

12

"NA""NA"

RFYielding4

1

12

"NA""NA"

Buckling Fastener Capacity

RBuckling4

1

12

26.5644.34

Ton RFastener4

1

12

11.8919.85

Ton

RFBuckling4

1

12

0.741.23

RFFastener4

1

12

0.330.55

01005_Gusset_U1_LFD_final Page 40 of 50

Page 41: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Gusset Plate Rating Summary (continued)

Section A-A Section B-B Section C-C

RVrAA

1

12

422.49705.24

Ton RVrBB

1

12

76.60127.86

Ton RVrCC

1

12

126.96211.92

Ton

RFVrAA

1

12

11.7419.59

RFVrBB

1

12

2.133.55

RFVrCC

1

12

3.535.89

01005_Gusset_U1_LFD_final Page 41 of 50

Page 42: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Truss Member Rating Summary

Left Diagonal - Member 1 - Tension or Compression Rating:

RmFastener1

1

12

22.036.8

Ton RmTen.block1

1

12

55.993.3

Ton

RFmFastener1

1

12

0.61.0

RFmTen.block1

1

12

1.62.6

Vertical - Member 2 - Tension or Compression Rating:

RmFastener2

1

12

33.155.2

Ton RmTen.block2

1

12

94.8158.2

Ton

RFmFastener2

1

12

0.91.5

RFmTen.block2

1

12

2.64.4

Right Diagonal - Member 3 - Tension or Compression Rating:

RmFastener3

1

12

20.734.5

Ton RmTen.block3

1

12

"NA""NA"

Ton

RFmFastener3

1

12

0.61.0

RFmTen.block3

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 42 of 50

Page 43: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Truss Member Rating Summary (continued)

Left Chord - Member 4 - Tension or Compression Rating:

RmFastener4

1

12

11.919.8

Ton RmTen.block4

1

12

"NA""NA"

Ton

RFmFastener4

1

12

0.30.6

RFmTen.block4

1

12

"NA""NA"

01005_Gusset_U1_LFD_final Page 43 of 50

Page 44: Mathcad - 01005 Gusset U1 LFD final 040609 PLATE LOAD RATING (LFD) - U1 ... While this Mathcad sheet has been checked, it should be used by an engineer familiar with truss and gusset

SO No.: 115231 Subject: VDOT BRIDGE RATING BRIDGE NO. 01005 - 1 SPAN TRUSS GUSSET PLATE LOAD RATING (LFD) - U1 Computed By: DLN Date: 10/07/2009 Checked By: MKB Date: 04/06/09

Controlling Gusset Plate Rating Summary

Gusset Plate Controlling Rating:

1 -Inventory2 -Operating

CaseConnInv 22.04 Ton ConnOpr 36.79 Ton

ConnInvF 0.61 ConnOprF 1.02

InvControlGusset "Member 1 Controls the Inventory Rating"

OprControlGusset "Member 1 Controls the Operating Rating"

InvRFControlGusset "Member 1 Controls the Inventory Rating Factor"

OprRFControlGusset "Member 1 Controls the Operating Rating Factor"

Truss Member Controlling Rating:

1 -Inventory2 -Operating

CaseConnmInv 22.04 Ton ConnmOpr 36.79 Ton

ConnmInvF 0.61 ConnmOprF 1.02

InvControlTrussMember "Truss Member 1 Controls the Inventory Rating"

OprControlTrussMember "Truss Member 1 Controls the Operating Rating"

InvRFControlTrussMember "Truss Member 1 Controls the Inventory Rating Factor"

OprRFControlTrussMember "Truss Member 1 Controls the Operating Rating Factor"

Operating Rating results shall be greater than HS 36 Tonotherwise structure requires posting according to VDOT guidelines

01005_Gusset_U1_LFD_final Page 44 of 50